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A company distributes its product by train and by truck. The cost of distributing by train can be modeled as −0.06x^2 + 32x − 100, and the cost of distributing by truck can be modeled as −0.04x^2 + 26x − 170, where x is the number of tons of product distributed. Write a polynomial that represents the difference between the cost of distributing by train and the cost of distributing by truck.

A −0.1x^2 + 6x − 270
B −0.02x^2 + 58x − 270
C −0.02x^2 + 6x + 70
D −0.02x^2 + 6x − 270

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GoddessofDork GoddessofDork · Answer 1 · 2018-12-07T19:29:39+01:00

So firstly, let's set up our equation. Since we are finding the difference between the 2 polynomials, this is going to be a subtraction problem:

[tex]-0.06x^2+32x-100-(-0.04x^2+26x-170)[/tex]

Next, foil -(-0.04x² + 26x - 170). (Treat the minus sign on the outside as -1):

[tex]-0.06x^2+32x-100+0.04x^2-26x+170[/tex]

Next, combine like terms:

[tex](-0.06x^2+0.04x^2)+(32x+(-26x))+(-100+170)\\-0.02x^2+6x+70[/tex]

In short, your final answer is C: -0.02x^2 + 6x + 70